Magnetic fields and relativistic electrons fill entire galaxy cluster

The hot plasma within merging galaxy clusters is predicted to be filled with shocks and turbulence that may convert part of their kinetic energy into relativistic electrons and magnetic fields generating synchrotron radiation. Analyzing Low Frequency Array (LOFAR) observations of the galaxy cluster Abell 2255, we show evidence of radio synchrotron emission distributed over very large scales of at least 5 megaparsec. The pervasive radio emission witnesses that shocks and turbulence efficiently transfer kinetic energy into relativistic particles and magnetic fields in a region that extends up to the cluster outskirts. The strength of the emission requires a magnetic field energy density at least 100 times higher than expected from a simple compression of primordial fields, presumably implying that dynamo operates efficiently also in the cluster periphery. It also suggests that nonthermal components may contribute substantially to the pressure of the intracluster medium in the cluster periphery.


Supplementary materials
Energy of non-thermal components. The observed synchrotron radiation in the cluster outskirts allows us to estimate an energy budget in the form of relativistic components. The energy density of particles and field is: where k is the energy ratio of relativistic protons and electrons. We assume a spectrum of relativistic electrons in the form: Of course, our observations do not allow us to measure this spectrum, yet we can safely assume that the real spectrum is matched by such a power law distribution at least in a suitable range around the energy of the electrons that are necessary to radiate at the frequencies where emission is detected; in particular, we note that synchrotron radiation at 49 MHz is generated by electrons with kinetic energy E kin ≈ 1.5B −1/2 µG GeV (that is γ ∼ 3000 for µG field level).
This implies min ∼ 2 × 10 −14 erg cm −3 , that should be compared to the thermal energy density measured in the same region ICM ∼ 3P e ∼ 4 × 10 −13 erg cm −3 (P e is provided in Fig. 4 of (13)). The magnetic field could be smaller if electrons have a larger energy budget, yet the total energy budget of the relativistic plasma will increase and become significant with respect to the thermal ICM.
Assuming a departure from minimum energy B = B min ∆, and using the condition K e B (δ+1)/2 = K e,min B (δ+1)/2 min (i.e. fixed synchrotron luminosity), the energy density is: consequently, adopting α = 1.6, B ∼ 0.1 µG (that is ∆ ∼ 0.2) would imply that relativistic electrons keep an energy budget similar to that of the ICM, that is an untenable condition; a similar conclusion is obtained for B ∼ 1.7 µG (that is ∆ ∼ 3.8) in which case the magnetic field would keep an energy budget similar to the ICM. Thus, the observed synchrotron radiation implies a lower limit of a few 0.1 µG, which is >10 times larger than the value of the primordial field compressed at a cosmic density ∼100 times the average value of the Universe. We note that our conclusions remain essentially the same, within a factor 2, if we adopt α ∼ 1.4 − 1.7 and γ min ∼ 1000 − 3000. to prevent that the minimum energy budget of non-thermal components matches the thermal energy budget. This simply implies that the observed spectrum of radio emitting electrons (with energies of a few GeV) cannot extend at energies ≤ several MeV, and thus that the radio emitting electrons are not accelerated from the thermal pool but extracted (re-accelerated) from a reservoir of particles that are already relativistic.
Electron acceleration and magnetic field amplification efficiencies. The observed synchrotron luminosity also allows us to derive constraints on the efficiency of magnetic field amplification and particle acceleration in the turbulent ICM; specifically we are interested on the possibility to obtain constraints at 1.5−2 Mpc distance from the cluster center where the steep spectrum envelope is observed.
If electrons are re-accelerated by turbulence in the ICM, the observed radiation is maintained by a fraction, η acc , of the turbulent kinetic energy flux that is transferred to particles and eventually radiated: where V is the emitting volume. As a consequence the fraction can be estimated from the observed synchrotron luminosity and from the turbulent energy flux that is measured in numerical simulations: The same turbulence can amplify the magnetic field via turbulent dynamo (17), which stretches and folds magnetic field lines as a consequence of turbulent motions. For large Reynolds numbers the amplification proceeds in a non-linear regime where the magnetic field (Reynolds stress) becomes dynamically important with respect to the turbulent motions on scales that are important for the amplification (20). In this case the magnetic field energy density grows linearly with time and the energy density that is converted into magnetic field in an eddy turnover time is: where τ edd ∼ Λ/σ v is the eddy turnover time and η B is the fraction of turbulent energy flux that is converted into field in an eddy turnover-time; η B ∼ 0.03 − 0.05 is measured in MHD simulations (18,20,59). Combining Eqs. S9 and S10 gives: that is used to obtain        Table S1: Resolution and noise of the 49 MHz (LBA) and 145 MHz (HBA) images produced in the paper.